各州不同

https://www.americanbar.org/content/dam/aba/migrated/leadership/fact_sheet.authcheckdam.pdf

这个更简单些：　原文在下面的连接

How state court judges are selected varies by state. States choose judges in any of the following ways:

• Appointment: The state's governor or legislature will choose their judges.
• Merit Selection: Judges are chosen by a legislative committee based on each potential judge's past performance. Some states hold "retention elections" to determine if the judge should continue to serve.
• Partisan Elections: Judges selected through partisan elections are voted in by the electorate, and often run as part of a political party's slate of candidates.
• Non-Partisan Elections: Potential judges that run for a judicial position in states with non-partisan elections put their names on the ballot, but do not list their party affiliates. Terms for judges in non-partisan elections can range between 6 and 10 years.

https://litigation.findlaw.com/legal-system/how-are-judges-selected.html